TMI safety both failed and succeeded depending upon how you look at things.
It failed to prevent a partial meltdown of the reactor core.
It failed to prevent a significant release of radiation to the general environment as 15 curies (560 GBq) of iodine-131 (the most concering portion due to biological uptake to the thyroid)
It succeeded in terms of avoiding the wide-scale problems of Fukushima or Chernobyl
It failed in terms of public opinion of nuclear power being a reasonably source of energy production. Nuclear plant construction in US was virtually shut down after this, no new licenses till 2012.